Measuring Optical Turbulence Using Cell Counting Algorithms

ABSTRACT

Methods for characterizing atmospheric turbulence along an optical path from a laser transmitter to a laser receiver can include the steps of counting the number of laser speckles at the receiver imaging plane, and then finding Fried&#39;s parameter r 0  using the counting result to characterize the turbulence along the path. Before counting speckles, images at the receiver image plane can be preprocessed by capturing the images. The captured images at the image plane can then be blurred and a threshold can be chosen so that only certain pixels in the image are further processed. The thresholding can be via Otsu&#39;s methods or via variants of a Gaussian fit. Kostelec&#39;s method can then be used to count speckles in the portions of the image that have made it through the thresholding step. Other counting methods could be used. Fried&#39;s can then be found using the speckle count.

FEDERALLY-SPONSORED RESEARCH AND DEVELOPMENT

The United States Government has ownership rights in this invention.Licensing inquiries may be directed to Office of Research and TechnicalApplications, Space and Naval Warfare Systems Center, Pacific, Code72120, San Diego, Calif., 92152; telephone (619) 553-5118; email:ssc_pac_t2@navy.mil, referencing NC 104223.

FIELD OF THE INVENTION

The present invention pertains generally to methods for characterizingatmospheric turbulence. More specifically, the present inventionpertains to methods for characterizing atmospheric turbulence along anoptical path. The invention is particularly, but not exclusively, usefulas methods for characterizing atmospheric turbulence along an opticalpath by counting laser speckles using interdisciplinary cell counttheories from the life sciences.

BACKGROUND OF THE INVENTION

Atmospheric turbulence, or refractive-index fluctuations, along the pathof a partially coherent beam can result in intensity fluctuations at thereceiving end of the propagation path. At the pupil plane this phenomenacan create a characteristic beam breakup, which can result in theappearance of “blobs” or “speckles” at the pupil plane, and which isreferred to in this paper as “speckles”, (as used herein, the term“speckles” is not to be confused with the speckle pattern created due tothe scattering of a beam from a rough surface). These intensityfluctuations can severely limit the performance of free-space opticalcommunication; thus, their characterization is of importance. One methodof measuring atmospheric turbulence is by estimating Fried's coherencelength, r₀, through its relationship with the number and size ofdiscrete speckles captured on an image plane after propagation through aturbulent field.

In the medical fields, “blob” identification is becoming an importantmeans of automating image analysis. These “blobs” can be representativeof cells, bacteria, etc., in various types of images, and countingmethods are able to count cells, detect blood vessel structures, mapbrain activity, and complete other manually tedious tasks. Consideringthe large effort put into optimizing these counting methods, theseinterdisciplinary counting techniques can be leveraged to quickly andeffectively count speckles in an image from the receiver of a lasercommunications systems. The speckles can be due to atmosphericturbulence, and if the speckles can be counted, the atmosphericconditions can be characterized, which can allow for additionalinformation such as maximum effective range of the communications systemto be characterized.

In view of the above, it can be an object of the present invention toprovide a method for characterizing atmospheric turbulence along anoptical path without using a scintillometer. Another object of thepresent invention can be to provide a method for characterizingatmospheric turbulence along an optical path by adapting cell countingmethods from the life sciences to count speckles along the optical path.Still another object of the present invention can be to provide a methodfor characterizing atmospheric turbulence along an optical path, inorder to gage the coherency of a laser beam in the turbulence. Yetanother object of the present invention to provide a method forcharacterizing atmospheric turbulence along an optical path that can beeasy to accomplish and use in a cost-effective manner.

SUMMARY OF THE INVENTION

Methods for characterizing atmospheric turbulence along an optical pathfrom a laser transmitter to a laser receiver can include the steps ofcounting the number of laser speckles at the receiver imaging plane, andthen finding Fried's parameter r₀ using the counting result tocharacterize the turbulence along the path. To the count speckles,images at the receiver image plane can be captured. The captured imagesat the image plane can then be blurred and a threshold can be chosen sothat only certain pixels in the image are further processed. Thethresholding can be via Otsu's methods or via variants of a Gaussianfit. Kostelec's method can then be used to count the portions of theimage that have made it through the thresholding step.

BRIEF DESCRIPTION OF THE DRAWINGS

The patent or application file contains at least one drawing executed incolor. Copies of this patent or patent application publication withcolor drawing(s) will be provided by the Office upon request and paymentof the necessary fee.

The novel features of the present invention will be best understood fromthe accompanying drawings, taken in conjunction with the accompanyingdescription, in which similarly-referenced characters refer tosimilarly-referenced parts, and in which:

FIG. 1 is a color photograph of a prior art cell embryo from the medicalfield, with characteristic beam breakup blobs, prior to a countingmethod being applied;

FIG. 2 is a color photograph of the embryo from FIG. 1, after a countingmethod has been applied;

FIG. 3 is a photograph of an image plane of an optical imaging systemwithout preprocessing steps of the present invention according toseveral embodiments being applied, and prior to the counting method ofFIG. 2 being applied;

FIG. 4 is the same photograph of FIG. 3, after the counting method ofFIG. 2 has been applied;

FIG. 5 is a block diagram, which illustrates steps that can be taken toaccomplish the methods of the present invention according to severalembodiments;

FIG. 6 is a graph of counts that can result using different thresholdswhen accomplishing the thresholding step using the methods of FIG. 5;

FIG. 7 is a histogram representation of the Gaussian thresholdingembodiments of the graph of FIG. 6;

FIG. 8 is the photograph of the same image plane as FIG. 3, but with thepreprocessing steps of the methods applied;

FIG. 9 is the same photograph as FIG. 8, after the counting methods havebeen applied;

FIG. 10 is a block diagram of the system of the present invention;

FIG. 11 is a prior art scatter plot of refractive indices, as measuredby a scintillometer vice the systems and methods for the presentinvention;

FIG. 12 if a prior art plot of the results of FIG. 11, at various timeintervals; and,

FIG. 13 is a comparison of the prior art results of FIG. 12 with thesystems and methods of the present invention.

DETAILED DESCRIPTION OF THE EMBODIMENTS

In brief overview, laser beam speckle at an image plane resulting fromatmospheric turbulence can contain information about the propagationchannel. The number and size of the speckles can be used to infer thespatial coherence and thus the refractive index, C_(n) ², along a path.The challenge with this technique is to be able to quickly and effectassess the rapidly evolving speckle pattern and non-uniformity of thespeckle cell and count the speckles. To do this, the speckles in animage plane can be analogized to “blobs” on an image in the medicalfield, such as cells, bacteria, etc. Modern blob counting techniquesused in biology, microscopy, and medical imaging can then be applied toturbulent speckle images, to estimate the number and size of the specklecells, and algorithms which can use the automated counting algorithmscan be generated to calculate path C_(n) ² from speckle information andpath geometry.

A. Fried's Coherence Length, r₀

As known in the optical prior arts, Fried's coherence length can be usedto characterize the effects of atmospheric turbulence on an opticalsystem. Primarily, it can describe system limitations on imageresolution due to atmospheric conditions, and can be defined as thediameter over which the time-average wave front error does not exceed 1radian. In the absence of atmosphere, an image formed at the focus of atelescope can have an angular resolution proportional to λ/D, where λ isthe wavelength of the source, and D is the aperture diameter of thereceiving optics.

Fried's coherence length (when expressed in terms of refractive indexstructure constant, c_(n) ², over a horizontal homogeneous path for aplane wave) can be given by Equation (1):

$\begin{matrix}{{r_{0} = \left\lbrack {1.67C_{n}^{2}k^{2}L} \right\rbrack^{- \frac{2}{5}}}{{{Where}\mspace{14mu} k} = \frac{2\; \pi}{\lambda}}} & (1)\end{matrix}$

is the wave number and L is the path length from source to receiver.

B. Fried's Parameter and Speckle Patterns

The number of speckles in an image of the pupil plane of an image systemcan be related to the aperture size of the imaging system and r_(o). Weapproximate the number of speckles by finding the ratio between the sizeof the seeing spot (the central spot of the diffraction pattern formedby interference of the wavefronts from the aperture) and the averagesize of a given speckle. As the resolution limit of the telescope underturbulence is limited by r₀, the size of the seeing spot is proportionalto

$\left( \frac{\lambda}{r_{0}} \right)^{2}.$

The separation of speckles is on the order of

$\frac{2\; \lambda}{D}$

and thus their area is proportional to

$\left( \frac{2\; \lambda}{D} \right)^{2}.$

Thus the number of speckles contained in the seeing spot can be given byEquation (2)

$\begin{matrix}{N = {{\left( \frac{\lambda}{r_{0}} \right)^{2}/\left( \frac{2\; \lambda}{D} \right)^{2}} = \left( \frac{D}{2\; r_{0}} \right)^{2}}} & (2)\end{matrix}$

Where N is the number of speckles. This equation relates the number ofspeckles to a ratio between lens area of aperture diameter D and aseeing spot having a circle of diameter λ/r₀. Intuitively, the number ofspeckles can be proportional to how many r₀ “areas” can fit on the lens.By counting the number of speckles contained in the seeing spot one cancalculate r₀, as indicated by Equation (3) below.

$\begin{matrix}{r_{0} = {\frac{D}{2}\sqrt{\frac{1}{N}}}} & (3)\end{matrix}$

Furthermore, the width of these speckles can be on the order of r₀ ³.

From the above, it can be seen that if the number of speckles can becounted at the seeing spot within the lens area, then Fried's number canbe determined. And once r₀ is determined, the atmospheric turbulencealong the path of transmission of a coherent laser beam can beestimated, which can further allow the user to estimate the coherency(effectiveness) of the laser beam, based on the distance through theatmosphere, the laser beam must travel through.

C. Blob Counting

In order to count the speckles, counting methods from interdisciplinaryfields can be used and adapted for the laser communications fields. Forexample, in the medical field, blobs identification and counting isbecoming an important means of automating image analysis (as usedherein, the term “blob” is used to define asymmetrical, non-uniformdistinguishable variations within an image). Thus, counting methods areable to count cells, detect blood vessel structures, map brain activity,and complete other manually tedious tasks. These algorithms can usemorphological operations to prepare the image and the watershedalgorithm to segment the structures, and these interdisciplinarycounting techniques can further be adapted for use in our countingspeckles in turbulent speckled images, as described more fully below.

The speckle counting algorithms of the present invention can be based ontwo cell counting algorithms, a basic cell counting and segmentationalgorithm described created by Pedro Kostelec and described in Kostelec,P., “Basic Cell Counting and Segmentation In Matlab” April 2014(hereinafter, the Kostelec counting method). Alternatively a cellcounting method used for counting stained cells in migration assays byBaraa K. Al-Khazraji and described in Al-Khazraji, B. K., et al., “AnAutomated Cell-Counting Algorithm For Fluorescently-Stained Cells InMigration Assays”. Biological Procedures Online, 13:9, October 2011(hereinafter, the Al-Khazraji counting method). The Kostelec andAl-Khazraji papers are hereby incorporated by reference herein.

In the medical/biological fields, cell counting algorithms can bedesigned to separate somewhat distinct areas. For example, and referringnow to prior art FIGS. 1-2, FIG. 1 can be a photograph of a cell assayof CAG::H2B-EGFP Tg/+ E10.5 (an embryonic stem cell from mice) before ablob counting method is applied, while FIG. 2 is a color photograph ofthe same cell assay after the counting method is applied. From comparingFIG. 1 to FIG. 2, it can be seen that the images are the same (otherthan a change in color), which can imply that the blob “count” has beenaccurately captured by the cell counting methods.

In contrast, FIGS. 3 and 4 are images of a lens area at a lasercommunications receiver before and after the same inter-disciplinarycell counting method used in FIG. 2 (the Kostelec method) has beenapplied. By cross-referencing FIGS. 1-2 and 3-4, it can be seen visuallythat the cell regions in FIGS. 1-2 are distinct, and can be “counted”much easier. This can be due to a more sharply defined contrast of thecell walls, which can facilitate the methods in distinguishing the blobfrom the background. On the other hand, and referring to FIGS. 3-4, theturbulent image offers no such help in finding such distinct regions.Furthermore, there are artifacts (reflections, debris, and aberrationsof the imaging system) present in the turbulent image which can bemisidentified as regions, or which can be incorrectly separated as asingle region. From the above, it is clear that the interdisciplinarycounting algorithm in its basic form can be unable to correctly separatethe turbulent regions and vastly over estimates their number. Thus, inorder for a cell counting algorithm from the life sciences to be appliedto characterize laser communications in turbulent atmospheres, the imagemust be preprocessed.

Referring now to FIG. 5, the methods of the present invention accordingto several embodiments can be depicted by block diagram 100. As shown,method 100 can include the steps of preprocessing the image, as shown bystep 101, followed by counting the number of N speckles 102 and findingFried's parameter r₀ using the speckles count N, as illustrated by step104. The methods can cheaply and effectively characterize atmosphericturbulence without the use of a costly and expensive scintillometer,which can be also be sensitive and difficult to use. But because of thelimitations in the lens image discussed above, the lens image must beprocessed to allow for counting methods to be used to count speckles.Stated differently, the lens image can be preprocessed to allow forspeckle counting.

In order to pre-process the image for counting, and as shown in FIG. 5,the image must be captured (step 106) and then blurred (step 108). Toaccomplish blurring step 108, the images can be passed through aGaussian blur filter which helps remove the aforementioned artifacts,while retaining the contrast between the speckles, each other, and thebackground.

Once the image has been blurred, and as shown by step 110 in FIG. 5, thenext preprocessing can be thresholding of the image. The thresholdingstep can limit the pixels from the lens image areas that the algorithmcan be used to calculate regions (and determine speckle count).Thresholding enhances the transition from background to turbulent cell,making the image more similar to the analogous cell assays where thecell wall can provide a sharp transition from background to “blob”, orcell. As the threshold pixel value for the thresholding step 100 can beincreased, the number of regions (speckles) which “make it through” andare counted by the counting algorithm can decrease in both size andnumber. However, and referring very briefly back to FIGS. 3 and 4, ifthe threshold level is set too low, the counting algorithm may not beable to distinguish from background, and an inaccurate cell count mayresult.

Using the guidelines above, a variety of thresholds can be used.Referring now to FIG. 6, a three-dimensional plot with counts that haveresult from using different thresholding limits is shown. FIG. 7 is ahistograph representation of the Gaussian fits of FIG. 6. The thresholdswere chosen by first representing the image as a histogram and allowingonly the counts above a certain value to be used in the countingalgorithm. From lowest to highest the threshold values were: Ostu's(plane 62); Full Width Half Max (plane 64); Full Width 90% Max (66); 1Sigma (68); and, 2 Sigma (70). Table 1 lists the algorithms used in FIG.6.

TABLE 1 Ostu's Otsu's method, MATLAB graythresh function, approximatelyseparates foreground from background FWHM All points above the lowerpoint of the full width half max of the Gaussian fit FW9M All pointsabove the lower point of the full width 90% max of the Gaussian fit 1Sigma All points above +1 sigma point of the Gaussian fit 2 Sigma Allpoints above +2 sigma point of the Gaussian fit

Four of the thresholding techniques were using Gaussian statistics. FIG.7 illustrates a Gaussian curve fit 72 to the image histogram (the largedistribution on the left of the plot 74 represents the area outside thecircular image as shown in FIG. 7, and the thresholding values can beseen as vertical lines 76-84, corresponding to (in order) Otsu's, FWHM,FW9M, 1 Sigma and 2 Sigma thresholding levels. After experimenting withthese thresholding techniques, it can be determined that Ostu's methodprovided turbulence values appeared to be closest to those measured byscintillometer. However, the other cell thresholding methods couldcertainly be used. Once an appropriate thresholding method is found thespots can be counted (step 102), and the calculated r₀ value can becalculated to describe optical turbulence, but without requiring ascintillometer.

Referring now to FIGS. 8-9. FIG. 8 is a photograph of the same lensimage of FIG. 3 after the preprocessing steps described above haveoccurred. FIG. 9 is a photograph after the same lens image after theKostelec counting method has been applied. By cross-referencing FIGS.8-9, and comparing to a cross-referencing of FIGS. 3-4, it can be seenthat the preprocessing steps has greatly facilitated the specklecounting. FIGS. 8 and 9 are essentially identical, which means that thecount and size of the speckles (if any) that are present is probablyaccurate. In comparison, from FIGS. 3 and 4 it can be seen that with nopreprocessing, the Kostelec method “over counts” speckles that arepresent. As can be seen from FIGS. 8 and 9, there is a drastic reductionin the number of erroneously counted regions after preprocessing of theimages.

D. Data Collection

Referring now to FIG. 10, a system in according with several embodimentsis shown and is generally designated with reference character 20. Asshown system 20 can include a laser source 22 and a laser receiver 24.Receiver 24 can include a lens system (telescope 26) with a mask 28 andan imaging lens 30. System 20 can further include a detector 32 and arecorder 34 for recording images. System 20 can also include a processor36. Processor 36 can include non-transitory instructions foraccomplishing the preprocessing sub-steps of the counting step detailedabove, as well as finding Fried's number r₀.

Telescope 26 can be a 150 mm F/5 (focal range of 5) telescope. Mask 28can be a 100 mm mask in combination with a 25 mm focal length imaginglens 30. Detector 32 can be a high resolution MAKO GigE camera,manufactured by ALLIED VISION®. Other high resolution cameras could beused. Recorder 36 can use STREAMPIX® (other streaming services could beused), and online video streaming service, to record images. Lasersource 22 can be a VSCEL (Vertical Cavity Surface Emitting Laser) arrayoperating at 1064 nm. The array can be a hexagonal package of laserswhich can produce a semi-coherent beam. To minimize any possible effectson data collection, laser output beam from source 22 can be routedthrough a 2 degree diffuser (not shown in FIG. 10). Typically, adiffuser can introduce its own beam speckle but due to the highturbulence during data collection these effects were minimal.

Operational test data was collected along a laser path with a distance Lof one kilometer. Data collection took place on over a three hour periodin later afternoon. Within the three hour period, the longest continuousdata collection period was over a 5 minute continuous period at 30frames per second. The exposure on the camera 32 was limited to ˜5 ms toprevent oversaturation and smearing of the turbulent images. The imageswere recorded at recorder 34 and formatted initially in a .seq fileformat and then exported as .png-formatted images before processing. ForComparison, a BLS900 scintillometer manufactured by Scintech was used torecord refractive indices C over the same laser path at 1 minuteintervals throughout the same data collection period. These results wereplotted as a scatter plot and can be seen in prior art FIG. 11.

E. Analysis and Results

All of the images collected over the 5 minute period were input into thecounting algorithm. The above-described preprocessing, Kosteleccounting, and Fried determinations steps were accomplished by theprocessor 36, and the output of the method the number of speckles ineach image was recorded. In order to compare to the BLS900 the number ofspeckles in the image needs to be converted into a C_(n) ² value, thiswas achieved by converting the number of speckles into r₀ usingEquations (2) and (3), and calculating. C_(n) ² by and rearrangingEquation (1) to express the refractive index structure constant in termsof Fried's coherence length, Equation (4):

$\begin{matrix}{C_{n}^{2} = \frac{r_{0}^{- \frac{5}{3}}}{1.67k^{2}L}} & (4)\end{matrix}$

Using this process, the C_(n) ² value for each image was calculated, andthen averaged over 1, 3, 10, and 30 second intervals, as shown in FIG.12. From FIG. 12, it can be seen that shorter averaging intervals offerslittle extra information and seem to converge to the long scaleaveraging values. Nevertheless, the 30 second average was used tocompare the different thresholding methods and compare against BLS900data.

Referring now to FIG. 13, the algorithms are tested on speckle imagesfrom experimental data collected over a turbulent 1 km path and comparedto C_(n) ² measurements collected in parallel. Otsu threshold preprocesssub-steps appears result in counts (132 in FIG. 13) that are closest tothe BLS900 data (134 in FIG. 13). However, it should be appreciated fromFIG. 13 that all of the thresholding methodologies 136-140 result incomparable count results, when compared to scintillometer data 134.Still further, none of the thresholding methods track the trend presentin the BLS900 data between 16:04 and 16:06, which was most like causedby discrepancies in optical source, wavelength, averaging time, and pathweighting could cause this effect. This could mean that the systems andmethods of the present invention can actually avoid some of the sourcesof error that can be inherent when using a scintillometer.

From the above, it can be seen that the systems and method of thepresent invention can accomplished very quickly (near-real time)measurement of r₀. Additionally, the methods could be compatible withany pupil plane imaging system/camera/wavelength (most scintillometersare designed to operate in a specific wavelength range). The systems andmethods could be adapted to incorporate new, future counting methodsthat may emerge. Still further, changes in hardware (camera, lensdiameter, focal length, and wavelength) could result in optimization ofcounting technique, while an increase in processing speed of processor36, can speed up the accomplishment of the preprocessing, counting andcalculating algorithms described above.

In addition to counting the speckles, the systems and methods can alsoincorporate the use of speckle size. This can be seen in more detail ina paper entitled “Blob Identification Algorithms Applied to LaserSpeckle to Characterize Optical Turbulence” by Galen D. Cauble, et al.The contents of the Cauble paper are hereby incorporated herein byreference

The use of the terms “a” and “an” and “the” and similar references inthe context of describing the invention (especially in the context ofthe following claims) is to be construed to cover both the singular andthe plural, unless otherwise indicated herein or clearly contradicted bycontext. The terms “comprising,” “having,” “including,” and “containing”are to be construed as open-ended terms (i.e., meaning “including, butnot limited to,”) unless otherwise noted. Recitation of ranges of valuesherein are merely intended to serve as a shorthand method of referringindividually to each separate value falling within the range, unlessotherwise indicated herein, and each separate value is incorporated intothe specification as if it were individually recited herein. All methodsdescribed herein can be performed in any suitable order unless otherwiseindicated herein or otherwise clearly contradicted by context. The useof any and all examples, or exemplary language (e.g., “such as”)provided herein, is intended merely to better illuminate the inventionand does not pose a limitation on the scope of the invention unlessotherwise claimed. No language in the specification should be construedas indicating any non-claimed element as essential to the practice ofthe invention.

Preferred embodiments of this invention are described herein, includingthe best mode known to the inventors for carrying out the invention.Variations of those preferred embodiments may become apparent to thoseof ordinary skill in the art upon reading the foregoing description. Theinventors expect skilled artisans to employ such variations asappropriate, and the inventors intend for the invention to be practicedotherwise than as specifically described herein. Accordingly, thisinvention includes all modifications and equivalents of the subjectmatter recited in the claims appended hereto as permitted by applicablelaw. Moreover, any combination of the above-described elements in allpossible variations thereof is encompassed by the invention unlessotherwise indicated herein or otherwise clearly contradicted by context.

What is claimed is:
 1. A method for characterizing free space opticalcommunication of a laser beam, said laser beam being transmitted from atransmitter to a receiver having an imaging plane, said methodcomprising the steps of: A) preprocessing an image from said imageplane; B) counting the number of laser speckles at said image; and, C)finding Fried's parameter r₀ using the result of said step B).
 2. Themethod of claim 1, wherein said step A) further comprises the steps of:A1) capturing said image; A2) blurring said image; A3) thresholding saidimage so that only certain speckles are counted.
 3. The method of claim2, wherein said thresholding step is accomplished using Otsu's method.4. The method of claim 2 wherein said thresholding step is accomplishedby using a Gaussian fit, and then selecting all points above the fullwidth, half max of said Gaussian fit.
 5. The method of claim 2 whereinsaid thresholding step is accomplished by using a Gaussian fit, and thenselecting all points above the full width, ninety percent maximum ofsaid Gaussian fit.
 6. The method of claim 2 wherein said thresholdingstep is accomplished by using a Gaussian fit, and then selecting allpoints above one standard deviation of the mean of the Gaussian fit. 7.The method of claim 2 wherein said thresholding step is accomplished byusing a Gaussian fit, and then selecting all points above two standarddeviations of the mean of the Gaussian fit.
 8. The method of claim 1,wherein said counting step is accomplished using Kostelec's method. 9.The method of claim 1, wherein said counting step is accomplished usingAl-Khazraji's method.
 10. A method for measuring refractive index alonga laser path of a laser beam, said laser beam being transmitted from atransmitter to a receiver having an image plane, said method comprisingthe steps of: A) preprocessing an image from said image plane; B)counting the number of laser speckles at said image; and, C) findingFried's parameter r₀ using the result of said step B).
 11. The method ofclaim 10, wherein said step A) further comprises the steps of: A1)capturing said image; A2) blurring said image; A3) thresholding saidimage so that only certain speckles are counted.
 12. The method of claim11, wherein said thresholding step is accomplished using Otsu's method.13. The method of claim 11 wherein said thresholding step isaccomplished by using a Gaussian fit, and then selecting all pointsabove the full width, half max of said Gaussian fit.
 14. The method ofclaim 11 wherein said thresholding step is accomplished by using aGaussian fit, and then selecting all points above the full width, ninetypercent maximum of said Gaussian fit.
 15. The method of claim 11 whereinsaid thresholding step is accomplished by using a Gaussian fit, and thenselecting all points above one standard deviation of the mean of theGaussian fit.
 16. The method of claim 11 wherein said thresholding stepis accomplished by using a Gaussian fit, and selecting all points abovetwo standard deviations of the mean of the Gaussian fit.
 17. The methodof claim 10, wherein said counting step is accomplished using Kostelec'smethod.
 18. The method of claim 10, wherein said counting step isaccomplished using Al-Khazraji's method.
 19. A system, comprising: atransmitter for transmitting a laser beam along a path; a receiverhaving an image plane; a recorder connected to said receiver forrecording images that result when said laser beam is incident on saidimage plane; and, a processor connected to said recorder, said processorhaving non-transitory instructions for counting the number of specklesin said image.
 20. The system of said claim 19, wherein said processoraccomplishes said counting using Kostelec's method.